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人気のある三角関数 >

cos^2(θ)=0.75

解

cos^{2} (θ) = 0.75

解

θ = 0.52359 \dots + 2 πn, θ = 2 π - 0.52359 \dots + 2 πn, θ = 2.61799 \dots + 2 πn, θ = - 2.61799 \dots + 2 πn

+1

度

θ = 3 0^{\circ} + 36 0^{\circ} n, θ = 329.99999 \dots^{\circ} + 36 0^{\circ} n, θ = 15 0^{\circ} + 36 0^{\circ} n, θ = - 15 0^{\circ} + 36 0^{\circ} n

解答ステップ

cos^{2} (θ) = 0.75

置換で解く

cos^{2} (θ) = 0.75

仮定:

cos (θ) = u

u^{2} = 0.75

u^{2} = 0.75 : u = 0.75, u = - 0.75

u^{2} = 0.75

x^{2} = f (a)

の場合, 解は

x = f (a), - f (a)

u = 0.75, u = - 0.75

代用を戻す

u = cos (θ)

cos (θ) = 0.75, cos (θ) = - 0.75

cos (θ) = 0.75, cos (θ) = - 0.75

cos (θ) = 0.75 : θ = arccos (0.75) + 2 πn, θ = 2 π - arccos (0.75) + 2 πn

cos (θ) = 0.75

三角関数の逆数プロパティを適用する

cos (θ) = 0.75

以下の一般解

cos (θ) = 0.75

cos (x) = a \Rightarrow x = arccos (a) + 2 πn, x = 2 π - arccos (a) + 2 πn

θ = arccos (0.75) + 2 πn, θ = 2 π - arccos (0.75) + 2 πn

θ = arccos (0.75) + 2 πn, θ = 2 π - arccos (0.75) + 2 πn

cos (θ) = - 0.75 : θ = arccos (- 0.75) + 2 πn, θ = - arccos (- 0.75) + 2 πn

cos (θ) = - 0.75

三角関数の逆数プロパティを適用する

cos (θ) = - 0.75

以下の一般解

cos (θ) = - 0.75

cos (x) = - a \Rightarrow x = arccos (- a) + 2 πn, x = - arccos (- a) + 2 πn

θ = arccos (- 0.75) + 2 πn, θ = - arccos (- 0.75) + 2 πn

θ = arccos (- 0.75) + 2 πn, θ = - arccos (- 0.75) + 2 πn

すべての解を組み合わせる

θ = arccos (0.75) + 2 πn, θ = 2 π - arccos (0.75) + 2 πn, θ = arccos (- 0.75) + 2 πn, θ = - arccos (- 0.75) + 2 πn

10進法形式で解を証明する

θ = 0.52359 \dots + 2 πn, θ = 2 π - 0.52359 \dots + 2 πn, θ = 2.61799 \dots + 2 πn, θ = - 2.61799 \dots + 2 πn

グラフ

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